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Which angle is not coterminal with the other three coterminal angles? 150°, 770°, 410°, -310° A. 150° C.-310° B. 410° D. 770°

Which angle is not coterminal with the other three coterminal angles? 150°, 770°, 410°, -310° A. 150° C.-310° B. 410° D. 770°

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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**Educational Content on Coterminal Angles** **Title: Identifying Coterminal Angles** --- **Question:** Which angle is not coterminal with the other three coterminal angles? 150°, 770°, 410°, -310° - A. 150° - B. 410° - C. -310° - D. 770° --- **Explanation:** Coterminal angles are angles that share the same terminal side when drawn in standard position. To determine if angles are coterminal, we can add or subtract multiples of 360° until we obtain an equivalent angle within the range of 0° to 360°. 1. **150°:** This angle is already within the range of 0° to 360°. 2. **770°:** Subtract 360° twice (770° - 360° - 360° = 50°). This angle is coterminal with 50°. 3. **410°:** Subtract 360° once (410° - 360° = 50°). This angle is coterminal with 50°. 4. **-310°:** Add 360° once (-310° + 360° = 50°). This angle is coterminal with 50°. We see that 410°, 770°, and -310° are all coterminal with 50°. Therefore, the angle that is not coterminal with the others is the angle that does not reduce to 50°. **Answer:** A. 150° --- **Source:** International Academy of Science. All Rights Reserved. --- This question teaches the concept of coterminal angles and how to determine if different angles are coterminal by manipulating them within the standard position range.
Transcribed Image Text:**Educational Content on Coterminal Angles** **Title: Identifying Coterminal Angles** --- **Question:** Which angle is not coterminal with the other three coterminal angles? 150°, 770°, 410°, -310° - A. 150° - B. 410° - C. -310° - D. 770° --- **Explanation:** Coterminal angles are angles that share the same terminal side when drawn in standard position. To determine if angles are coterminal, we can add or subtract multiples of 360° until we obtain an equivalent angle within the range of 0° to 360°. 1. **150°:** This angle is already within the range of 0° to 360°. 2. **770°:** Subtract 360° twice (770° - 360° - 360° = 50°). This angle is coterminal with 50°. 3. **410°:** Subtract 360° once (410° - 360° = 50°). This angle is coterminal with 50°. 4. **-310°:** Add 360° once (-310° + 360° = 50°). This angle is coterminal with 50°. We see that 410°, 770°, and -310° are all coterminal with 50°. Therefore, the angle that is not coterminal with the others is the angle that does not reduce to 50°. **Answer:** A. 150° --- **Source:** International Academy of Science. All Rights Reserved. --- This question teaches the concept of coterminal angles and how to determine if different angles are coterminal by manipulating them within the standard position range.
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